You can apply for an emergency travel document if you’re abroad, need to travel and cannot get a passport in time, and if all the following apply:
- you’re a British national
- you’re outside the UK
- your passport has been lost, stolen, damaged, is full, has recently expired or is with HM Passport Office or a foreign embassy
- you do not have time to renew or replace your passport before you travel
- you can provide proof of your travel plans, for example booking confirmations (or detailed written travel plans if you cannot book ahead)
You have to apply online so I can’t ascertain whether you have to provide the reason why you need an ETD. But on the assumption that you do, given that forgetting or leaving your passport at home are not listed under the eligibility criteria, I’d say the answer to your question is ‘no’.
Lying that you lost your passport is pointless anyway, since you are required to cancel a lost or stolen passport https://www.gov.uk/report-a-lost-or-stolen-passport